In this article, we study the asymptotical limits of error correction for the paradigm of time-varying quantum channel models. Motivated by the similarity between the TVQCs and classical slow or block fading scenarios, i.e., when the channel remains constant over the duration of the coded block [1]}, [2]}; we define the quantum outage probability of a TVQC as the asymptotically achievable error rate for a QECC with quantum rate \(R_\mathrm {Q}\)  that operates over the aforementioned noise model. Additionally, we also introduce the concept of the quantum hashing outage probability to provide an upper bound on the asymptotically achievable error rate for TVQC channels whose quantum capacity (of their static counterparts) is unknown, but for which a lower bound known as the hashing limit exists. Based on the experimentally determined statistical distribution of \(T_1\)  [1]}, [4]}, we provide closed-form expressions for the known TVQCs: time-varying amplitude damping channel (TVAD), time-varying amplitude damping Pauli twirl approximated channel (TVADPTA) and time-varying amplitude damping Clifford twirl approximated channel (TVADCTA). We analyze the quantum outage probability and quantum hashing outage probabilities of the aforementioned TVQCs for different scenarios. Finally, QTCs operating over the considered channels are numerically studied and benchmarked using the derived information theoretic limits.
